On the Goncharov Depth Conjecture and polylogarithms of depth two

Steven Charlton; Herbert Gangl; Danylo Radchenko; Daniil Rudenko

paper

On the Goncharov Depth Conjecture and polylogarithms of depth two

arXiv:2210.11938

Abstract

We prove the surjectivity part of Goncharov's depth conjecture. We also show that the depth conjecture implies that multiple polylogarithms of depth $d$ and weight $n$ can be expressed via a single function $Li_{n - d + 1, 1, \dots, 1} (a_{1}, a_{2}, \dots, a_{d})$ , and we prove this latter statement for $d = 2$ .

4 pages, added Corollary 6, title modified to emphasise result on Depth Conjecture